Kink instability in circular DNA studied as Helfrich chiral chains

The mechanism of kink instability observed in short DNA circles [W. Han et al., Nature (London) 386, 563 (1997)] has been analyzed based on the model of chiral elasticity for helical fibers proposed by Helfrich [Langmuir 7, 567 (1991)]. It is shown theoretically that the circle is the planar solution of the equilibrium shape equations derived within this model and its stability is studied as the function of the elastic moduli of DNA. It is found that above some thresholds of the chiral modulus, $k_3,$ the circular DNA can be deformed into elliptical, triangular, square, or other polygonal shapes. The predicted shape transformation is found in good agreement with the above kink instability observed in DNA.